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A NEW CHARACTERIZATION OF GEODESIC SPHERES IN THE HYPERBOLIC SPACE.
- Source :
-
Proceedings of the American Mathematical Society . Jul2016, Vol. 144 Issue 7, p3077-3084. 8p. - Publication Year :
- 2016
-
Abstract
- This paper gives a new characterization of geodesic spheres in the hyperbolic space in terms of a "weighted" higher order mean curvature. Precisely, we show that a compact hypersurface Σn-1 embedded in ℍn with VHk being constant for some k = 1, · · ·, n - 1 is a centered geodesic sphere. Here Hk is the k-th normalized mean curvature of Σ induced from Hn and V = coshr, where r is a hyperbolic distance to a fixed point in ℍn. Moreover, this result can be generalized to a compact hypersurface Σ embedded in Hn with the ratio V (Hk/Hj) ≡ constant, 0 ≤ j < k ≤ n - 1 and Hj not vanishing on Σ. [ABSTRACT FROM AUTHOR]
- Subjects :
- *GEODESICS
*HYPERBOLIC spaces
*CURVATURE
*GEODESIC spaces
*HYPERSURFACES
Subjects
Details
- Language :
- English
- ISSN :
- 00029939
- Volume :
- 144
- Issue :
- 7
- Database :
- Academic Search Index
- Journal :
- Proceedings of the American Mathematical Society
- Publication Type :
- Academic Journal
- Accession number :
- 114700133
- Full Text :
- https://doi.org/10.1090/proc/12325